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A133847 a(n)*a(n-9) = a(n-1)*a(n-8)+a(n-4)+a(n-5) with initial terms a(1)=...=a(9)=1. 6
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 9, 13, 21, 33, 49, 169, 293, 421, 553, 823, 1365, 2179, 3265, 11289, 19585, 28153, 36993, 55081, 91393, 145929, 218689, 756163, 1311861, 1885783, 2477929, 3689557, 6121925, 9775033, 14648881, 50651601, 87875061 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..4390

P. Heideman and E. Hogan, A New Family of Somos-Like Recurrences, arXiv:0709.2529 [math.CO], 2007-2009.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,68,0,0,0,0,0,0,0,-68,0,0,0,0,0,0,0,1).

FORMULA

Sequence also generated by the linear recurrence 68*(u(n-8)-u(n-16))+u(n-24) with the initial 24 terms given by the quadratic recurrence.

G.f.: x*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 -67*x^8 -65*x^9 -63*x^10 -61*x^11 -59*x^12 -55*x^13 -47*x^14 -35*x^15 +49*x^16 +33*x^17 +21*x^18 +13*x^19 +9*x^20 +7*x^21 +5*x^22 +3*x^23) / ((1 -x)*(1 +x)*(1 +x^2)*(1 +x^4)*(1 -67*x^8 +x^16)). - Colin Barker, Jul 18 2016

MAPLE

a := proc(n) option remember; if n<=9 then RETURN(1); else RETURN((a(n-1)*a(n-8)+a(n-4)+a(n-5))/a(n-9)); fi; end;

MATHEMATICA

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]==a[8]==a[9]==1, a[n]==(a[n-1]a[n-8]+a[n-4]+a[n-5])/a[n-9]}, a, {n, 50}] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 9, 13, 21, 33, 49, 169, 293, 421, 553, 823, 1365, 2179}, 50] (* Harvey P. Dale, Jan 14 2016 *)

PROG

(PARI) a(k=9, n) = {K = (k-1)/2; vds = vector(n); for (i=1, 2*K+1, vds[i] = 1; ); for (i=2*K+2, n, vds[i] = (vds[i-1]*vds[i-2*K]+vds[i-K]+vds[i-K-1])/vds[i-2*K-1]; ); for (i=1, n, print1(vds[i], ", "); ); } \\ Michel Marcus, Nov 01 2012

(PARI) Vec(x*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 -67*x^8 -65*x^9 -63*x^10 -61*x^11 -59*x^12 -55*x^13 -47*x^14 -35*x^15 +49*x^16 +33*x^17 +21*x^18 +13*x^19 +9*x^20 +7*x^21 +5*x^22 +3*x^23) / ((1 -x)*(1 +x)*(1 +x^2)*(1 +x^4)*(1 -67*x^8 +x^16)) + O(x^50)) \\ Colin Barker, Jul 18 2016

CROSSREFS

Cf. A072881, A092264, A133846, A133848, A133854.

Sequence in context: A211139 A089228 A262602 * A134180 A107220 A249412

Adjacent sequences: A133844 A133845 A133846 * A133848 A133849 A133850

KEYWORD

easy,nonn

AUTHOR

Emilie Hogan, Sep 26 2007

STATUS

approved

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Last modified November 27 19:48 EST 2022. Contains 358406 sequences. (Running on oeis4.)